Explore quantum information phases in space-time through a 43-minute lecture by Vedika Khemani at the International Centre for Theoretical Sciences. Delve into measurement-induced entanglement and related topics as part of the program on "Stability of Quantum Matter in and out of Equilibrium at Various Scales." Gain insights into many-body quantum systems, their coherent time evolution, and the deep questions surrounding quantum matter behavior. Examine mechanisms constraining many-body dynamics in Hilbert space, including Many-body localization, Floquet MBL, Dynamical Freezing, and Hilbert Space Fragmentation. Learn about the interdisciplinary nature of this research, drawing from Condensed Matter Physics, Statistical Mechanics, Quantum Field Theory, and Mathematics. Understand the implications for quantum devices and the broader field of quantum technologies.